Heating control stops guessing from fixed thermometers: a time-free PINN holds room temperature fields within 1.85% error
Synopsis
Indoor heating usually relies on one or a few fixed-point temperature readings, which miss the spatial variation around an occupant. A physics-informed neural network drops time as an explicit input and instead infers how the temperature field evolves from spatial coordinates plus a few sensor readings and their rates of change; across nine horizontal planes in three room-scale configurations it matched a validated COMSOL multiphysics simulation with a maximum relative error below 1.85%. Wired into occupant-centric heating control, it showed an average numerical error of about 0.67% against COMSOL-based offline control, with inference fast enough for real-time use.
Interpretation
Space heating control starts using the local temperature at the occupant's position as feedback instead of one or a few fixed-point readings in the room. Earlier occupant-centric heating control depended on computationally intensive multiphysics simulation and licensed commercial software, which limited real-time deployment. Across nine horizontal planes in three room configurations, predicted temperature fields were compared with a validated COMSOL multiphysics simulation, and the maximum relative error in validation cases stayed below 1.85%.
The model no longer takes time as an input and instead infers how the temperature field changes over time from spatial coordinates and sensor readings. Conventional physics-informed neural networks take absolute time as an input, so the learned solution is tied to the initial conditions and disturbance trajectories seen in training. Four indoor temperature sensors record continuously; a first-order finite difference estimates the time derivative at each sensor, and the chain rule with automatic differentiation folds that rate into the residual loss of the heat-conduction equation.
With the same controller and only the temperature-field estimator swapped from COMSOL to the trained network, control decision time falls from about 8.8 hours to about 1 minute. The COMSOL version needed 31,923.91 seconds for a 3-hour simulation case, about 2.93 times real time. The PINN version finished the same 3-hour case in 60.69 seconds, about 0.56% of real time, and the two differed along the occupant's activity trajectory by a maximum numerical error of 2.46% and an average of 0.67%.
Perspective
Validation covers a laboratory kitchen room and two configurations scaled to 80% and 120% of its dimensions, nine horizontal planes in total, benchmarked against a previously experimentally validated COMSOL multiphysics model; the control evaluation is a single 3-hour simulation with a randomly selected occupant activity trajectory.
Point temperature on a horizontal plane is explicitly framed as a control-oriented approximation rather than a complete three-dimensional comfort metric; the authors also note that deployment on lower-performance real controllers remains to be validated, and sensor failures and data reliability have not yet been systematically analysed.